year 6 problem solving lessons

35 year 6 maths questions

Practise 35 year 6 maths questions that will help your child stay on track!

Author Amber Watkins

Published February 2024

Key takeaways
Year 6 maths word problems help students apply mathematical concepts to real-world scenarios.
In year 6 maths, it’s important to master fractions, decimals, and order of operations.
Hard problems can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

Word problems
Numbers & place value

Multiplication

If this maths page has 5 sections of maths questions with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 year 6 maths questions for us to practise. Without realising it, you just solved one of our first year 6 word problems . Excellent work! Together we will review year 6 maths problems with decimals, fractions, order of operations, and rounding. We will even consider hard maths problems, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Year 6 maths word problems

Let’s begin by covering maths word problems.

Mia’s water bottle can hold 300 millilitres of water. She drinks two and a half water bottles each day. How many total millilitres of water does Mia drink each day?

The playground is made up of four rectangular lots that are each 10 metres by 7 metres. What is the total area of the playground?

Josh lives 2.5 kilometres away from the park. Josh rides his bike to the park and back home four days a week. How many kilometres does Josh ride his bike each week?

Since we are solving word problems, a word should always be in our answer.

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Numbers & place value

In this section, we will cover maths questions that use place values, word form to standard form, standard form to word form, and expanded form.

Place value

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

In this section, we will cover year six maths questions that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review maths questionss for year six that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations.

Adding and subtracting whole numbers by transformation

A large portion of year 6 maths problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practise adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate!

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320- 200 = 120 The answer is 120

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

$year 6 problem solving lessons$

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Remember that the steps Multiply or Divide can be done in any order. Also, the steps Add or Subtract can be done in any order, do the operation that comes first.

Some of the hardest maths questions involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practise a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

$year 6 problem solving lessons$

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

For more maths practice for year 6 , our app for maths help provides year 6 maths help in a way that makes maths fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on maths topics they struggle with. Check it out today !

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

Word problem answer sheet

Mia drinks 750 millilitres of water each day.

Explanation: 300 x 2 = 600. 300 / 2 = 150. 600 + 150 = 750.

280 square metres.

Explanation: The area of one lot is 10 x 7 = 70 metres. Take that area and times it by four, so 70 x 4 = 280 metres.

Josh rides 20 kilometres on his bike each week.

Explanation: Each day Josh rides 5 total kilometres: 2.5 kilometres to the park and 2.5 kilometres back home. If we multiply that number by 4 days a week, it equals 20 kilometres in all.

Writing numbers answer sheet

2 is in the hundreds place.

$year 6 problem solving lessons$

0 is in the tens place.

$year 6 problem solving lessons$

2 is in the ones place.

$year 6 problem solving lessons$

Division using area models answer sheet

$year 6 problem solving lessons$

Multiplying using square models answer sheet

$year 6 problem solving lessons$

Multiplying fractions and whole numbers using expanded form answer sheet

$year 6 problem solving lessons$

Multiplying fractions using a number line answer sheet

$year 6 problem solving lessons$

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓.

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring students in maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Year 6 Maths Worksheets and Teaching Resources

Year 6 is a big and exciting school year for children. Just like each year of primary education, Year 6 brings new challenges and interesting lessons, but it also leads up to a big stage in children’s lives: theYear 6 transition to secondary school.

So this last year of primary school will prepare not-so-little ones for the move up to “big school” with more complex lessons, independent learning experiences and discussions about what to expect during the transition.

Before moving up to Key Stage 3, children will need a good understanding of the foundational knowledge learned during both KS1 and KS2, so in addition to delving deeper into upper KS2, children in Year 6 will revise earlier topics to build their mathematical fluency.

And when it comes to helping children consolidate their knowledge and grasp new topics in the Year 6 maths curriculum, we’re here to help. At Master the Curriculum, you’ll find fun and engaging Year 6 maths worksheets and resources of all kinds, including interactive maths videos, reasoning booklets, teaching slides and more. With our resources, you can help children master primary maths and spark excitement for learning in young minds.

Year 6 White Rose Maths Resources: Help Children Master Primary Maths

Here at Master the Curriculum, we’re big supporters of White Rose Maths (WRM). And just like WRM, we want to help children develop a deep and lasting understanding of maths concepts and find enjoyment in mathematical challenges. All of our resources are aligned with this approach so that children are ready and keen to grasp more advanced topics when they transition to secondary school.

We’ve designed our resources for maths mastery, which is why each has a learning objective that matches one of the small steps to progression. For example, you might find resources with learning objectives like “Calculate and interpret the mean as an average” or “Find pairs of numbers that satisfy an equation with two unknowns”. This makes it easy for you to find learning materials that are suited to children’s abilities and help pupils move through topics in a logical order. But the benefits of using our Year 6 maths resources for White Rose lessons don’t stop there.

Just like the WRM curriculum, our Year 6 maths worksheets and learning materials revolve around three main types of activities: reasoning, problem-solving and fluency. Why? Because by tackling these types of tasks, children deepen their mathematical understanding, develop their numeracy skills and consolidate their knowledge.

White Rose Maths is also about making maths enjoyable, so we make all of our resources engaging and fun! We know that children learn and retain information best when they have a smile on their face, and in Year 6 especially, youngsters need to remember the lessons they learn so that they can jump into Year 7 maths with confidence.

So with our Year 6 White Rose-style resources, you can make sure children are fully prepared and have all of the foundational knowledge and skills they need to succeed in secondary school maths lessons and beyond.

Want to learn more about our White Rose resources? Check out our Supporting White Rose Maths Hub.

The Year 6 Maths Curriculum: What Will Children Learn?

Our resources are perfectly aligned with the national curriculum. Each and every learning resource we offer has been carefully designed to help children meet a specific learning objective within one of the eight key topics laid out by the Department of Education’s Year 6 programme of study:

Number and Place Value — Throughout Year 6, children will become acquainted with numbers beyond 1,000,000 and up to 10,000,000. They will learn to read, write, order and compare numbers up to 10,000,000 and round any whole number to a required degree of accuracy. They will also need to use negative numbers in context and calculate intervals across zero.
Addition, Subtraction, Multiplication and Division — Using written methods of calculation, children will be taught to multiply and divide numbers with up to four digits by two-digit whole numbers. They will also build their mental maths skills, solve problems using all four operations and learn to check their answers using estimation.
Fractions — Year 6 lessons on fractions will teach children to apply all four operations to fractions. Children will add and subtract fractions with different denominators using equivalent fractions, multiple pairs of proper fractions and divide proper fractions by whole numbers. They will also learn equivalences between fractions, decimals and percentages.
Algebra — Year 6 is the first taste children will get of algebra, a key part of Key Stage 3 maths. During this year, they’ll be introduced to simple formulae and will learn to generate and describe linear number sequences, express missing numbers algebraically and find pairs of numbers that satisfy equations with two unknowns.
Geometry — By the end of the school year, children will be able to draw 2D shapes using given dimensions and angles and build simple 3D shapes. They will also be able to compare and classify geometric shapes and find unknown angles, and come to grips with more advanced concepts, such as the radius, diameter and circumference of circles, and coordinates plotted on a full coordinate grid.
Measurement — Children will develop their understanding of different types of measurements by learning to convert units of measurement, and measurements of length, time, mass and volume using decimal notation up to three decimal places. They will also continue learning about perimeter, area and volume, and use formulae where possible to calculate area and volume.
Ratio and Proportion — Year 6 maths will teach children more about the relationship between two numbers. They will learn to recognise proportionality in different contexts and solve problems using scale factors, unequal properties (for example, “For every three green apples, four are red. What fraction of the apples are green?”). They’ll also learn to use percentages to calculate angles of pie charts.
Statistics — Children will develop their ability to understand and present data by interpreting and construction pie charts and line charts, as well as learn how to calculate and interpret the mean as average.

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Reasoning Maths resources

What Types Of Year 6 Teaching Resources Do We Offer?

How Our Teacher-approved Resources Can Help

As a team of teachers, we know that the Year 6 maths curriculum can present children with maths concepts and problems that are particularly tricky to grasp. But we’re firm believers that every child can become a maths whizz with the right support and resources. Our resources are designed to help all children overcome obstacles to learning, achieve maths mastery and find enjoyment in maths lessons.

Whether you’re a teacher looking for resources to enhance your lesson plans or a parent looking for primary maths resources for home learning, you can use our learning materials to improve children’s understanding of complex concepts and boost their confidence in their maths abilities.

Enable Deeper Learning with the Right Resources

We offer resources of varying levels of difficulty that give children the chance to apply their maths knowledge, reasoning skills and problem-solving abilities to different contexts. In doing so, they’ll need to consider different methods and ways to approach maths problems, and as a result, they’ll gain a deeper understanding of mathematical concepts.

Encourage Children to Embrace Independent Learning

By encouraging children to independently complete the tasks laid out in our resources, you can prepare them for the more independent learning style they’ll need to embrace in secondary school.

We also offer mini-assessments complete with answers and worksheets to help children practise using estimation to check their answers to calculations. These resources can introduce children to reflective learning and self-assessment, which will be a common feature in secondary education.

Introducing children to these practices in Year 6 can help them develop their independence and sense of responsibility before moving up to KS3. It can also encourage deeper learning, as children will have the opportunity to better understand and improve their learning.

Engage and Excite Children with Fun Maths Resources

As well as helping children practise their maths skills, our resources use visual elements, fun activities and creative contexts to capture children’s attention and encourage them to have fun with maths.

Making maths enjoyable for children is particularly important during this year, as children will be tackling tricky topics. Challenging maths problems can cause children to become frustrated and disengaged with lessons, but if lessons are fun and even exciting, students will be more willing to participate and give it their best shot. Having fun while learning can also promote a deep and lasting mathematical understanding, as when lessons are more memorable, children are more likely to retain the information learned.

Gain Access To Hundreds Of Year 6 Maths Resources

Free Membership : We want to make sure all children have access to the resources they need to master maths and have fun doing so, so we’ve made many of our resources available completely free of charge. All you need is a free account. Once you’ve signed up, you can start downloading free worksheets straight away.
Year 6 Membership : If you want to access all of our Year 6 resources, both free and premium, you can sign up for a Year 6 membership for just £55 a year! With this membership, you can use, download and print as many of our Year 6 resources as you like.
Full Access Membership : Our full access membership is perfect if you have children in different primary year groups or you teach primary school children of different ages. You don’t need to purchase different year group memberships — instead, you can unlock access to thousands of resources across all primary year groups for just £77 per year.

Browse Year 6 Maths Worksheets And Resources By Topic

You can find Year 6 maths worksheets and resources that are perfectly suited for your lessons by browsing resources by topic. Find learning materials to accompany your lesson plans and help children meet learning objectives with a variety of resources, including highly visual worksheets, teaching slides, reasoning booklets and assessments.